Download App

Relation — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSRelation4 Marks
Question
If A = {1, 2, 3}, B = {4}, C = {5}, then verify that: $\text{A}\times(\text{B}\cup\text{C})=(\text{A}\times\text{B})\cup(\text{A}\times\text{C})$
✓

Answer

We have, $\text{A}=\{1,2,3\}\times\{4\}$ $\therefore\ \text{B}\cup\text{C}=\{4\}\cup\{5\}=\{4,5\}$ $\therefore\ \text{A}\times(\text{B}\cup\text{C})=\{1,2,3\}\times\{4,5\}$ $\Rightarrow\text{A}\times(\text{B}\cup\text{C})=\{(1, 4), (1, 5), (2, 4), (2, 5), (3, 4), (3, 5)\}\ ...(\text{i}) $ Now, $\text{A}\times\text{B}=\{1, 2, 3\}\times\{4\}$ $=\{(1, 4), (2, 4), (3, 4)\}$ and, $\text{A}\times\text{C}=\{1,2,3\}\times\{5\}$ $=\{(1, 5) , (2, 5), (3, 5)\}$ $\therefore\ (\text{A}\times\text{B})\cup(\text{A}\times\text{C})=\{(1, 4), (2, 4), (3, 4)\} \cup\{(1, 5), (2, 5), (3, 5)\}$ $\Rightarrow(\text{A}\times\text{B})\cup(\text{A}\times\text{C})=\{(1,4), (1,5), (2, 4), (2, 5), (3, 4), (3, 5)\}\ ...(\text{ii})$ From equation (i) and (ii), we get $\text{A}\times (\text{B}\cup\text{C})=(\text{A}\times\text{B})\cup(\text{A}\times\text{C})$ Hence verified.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "(Each question 4 marks)" from Relation→Relation — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Evaluate the following limit: $\lim\limits_{\text{x}\rightarrow0}\frac{(1+\text{x})^{{6}}-1}{(1+\text{x})^2-1}$
→
Find sets A, B and C such that $\text{A}\cap\text{B},\text{ A}\cap\text{C and B}\cap\text{C}$ are non-empty sets and $\text{A}\cap\text{B}\cap\text{C}=\phi.$
→
Evaluate the following limit: $\lim\limits_{\text{x}\rightarrow{\frac{\pi}{4}}}\frac{\sqrt{2}-\cos\text{x}-\sin\text{x}}{\big(\frac{\pi}{4}-\text{x}\big)^2}$
→
If $\Big(\frac{1-\text{i}}{1+\text{i}}\Big)^{100}=\text{a}+\text{ib},$ find (a, b).
→
For the function$\text{f}(\text{x})=\frac{\text{x}^{100}}{100}+\frac{\text{x}^{99}}{99}+...+\frac{\text{x}^2}{2}+\text{x}+1.$
Prove that $\text{f}'(1)=100$$\text{f}'(0)$.
→
A sequence $a_1, a_2, a_3,$ ... is defined by letting $a_1 = 3$ and $a_k = 7a_k - 1$ for all natural numbers $\text{k}\geq2.$ Show that $a_n = 3.7^{n-1}$ for all $\text{n}\in\text{N}.$
→
Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers): $\frac{\text{ax+b}}{\text{cx+d}}$
→
If a, b, c are in G.P., prove that: $(\text{a}+2\text{b}+2\text{c})(\text{a}-2\text{b}+2\text{c})=\text{a}^2+4\text{c}^2$
→
A line is such that its segment between the straight lines 5x - y - 4 = 0 and 3x + 4y - 4 = 0 is bisected at the point (1, 5). Obtain its equation.
→
Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse. $\frac{\text{x}^2}{16}+\frac{\text{y}^2}{9}=1$
→